Cauchy problem for NLKG in modulation spaces with noninteger powers

2014/11/13 by Qiang Huang, Qiang, Huang, Dashan, Fan +2 · 1 citation
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Mathematical Analysis and Transform Methods #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1411.3535

Abstract

In this paper, we consider the Cauchy problem for the nonlinear Klein-Gordon equation whose nonlinearity is |u|^ku in the modulation space, where k is not an integer. Our method can be applied to other equations whose nonlinear parts have regularity estimates. We also study the global solution with small initial value for the Klein-Gordon-Hartree equation. By this we can show some advantages of modulation spaces both in high and low regularity cases.

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• Superposition in Modulation Spaces with Ultradifferentiable Weights

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